Geodesic
Spatial patterns for reaction-diffusion systems with conditions described by inclusions
Applications of Mathematics, Tome 42 (1997) no. 6, pp. 421-449

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We consider a reaction-diffusion system of the activator-inhibitor type with boundary conditions given by inclusions. We show that there exists a bifurcation point at which stationary but spatially nonconstant solutions (spatial patterns) bifurcate from the branch of trivial solutions. This bifurcation point lies in the domain of stability of the trivial solution to the same system with Dirichlet and Neumann boundary conditions, where a bifurcation of this classical problem is excluded.
DOI : 10.1023/A:1022203129542
Classification : 35B32, 35J85, 35K57, 35K58, 35K85, 47H04, 47H15, 47N20
Keywords: reaction-diffusion systems; variational inequalities; inclusions; bifurcation; stationary solutions; spatial patterns 
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     title = {Spatial patterns for reaction-diffusion systems with conditions described by inclusions},
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Eisner, Jan; Kučera, Milan. Spatial patterns for reaction-diffusion systems with conditions described by inclusions. Applications of Mathematics, Tome 42 (1997) no. 6, pp. 421-449. doi: 10.1023/A:1022203129542

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